Are you the admin on your Teams team? Do you have access to the Advanced Directory/Azure Domain controls?

If not, you're going to have to have an admin do any kind of set up of that type.

The first major issue is that looks like most download controls in Teams are on a per-user basis, meaning that the easiest way to block downloads is to deny the user access from downloading entirely.

It seems like there are options for Android management that allow you to block an Android device from downloads as well.

https://learn.microsoft.com/en-us/mem/intune/apps/app-protection-policy-settings-android

But I can't seem to find anything on blocking specific other devices from downloads, and all the stuff I'm digging up circles back around to blocking the user from downloading entirely, instead of blocking them on a per-device level.

https://answers.microsoft.com/en-us/msteams/forum/all/how-to-block-users-from-downloading-files-in-the/b042e974-6c41-4df9-86b2-dedd0908f034

This one shows that they have admin options like this:

"5. Under "Actions", select "Block access" and choose the conditions you want to apply (e.g. "Block access when user is outside of company network")."

So perhaps in the admin settings there's more fine-grained options like this? I still don't see references to blocking per-device, just stuff like being outside the enterprise network.

https://old.reddit.com/r/Office365/comments/nxmob0/block_files_downloads_in_ms_teams_desktop_and_web/

This makes it sound like the solution is actually in SharePoint

https://learn.microsoft.com/en-us/answers/questions/1527066/how-i-can-restrict-to-download-content-from-micros

This is the closest I found to an answer, and it still seems like it's not 100% of what you're asking for, but maybe?